This set of Aptitude Questions and Answers (MCQs) focuses on “Functions”.
1. Given log 3 = 0.4771, then what would be the value of (log (0.27)2 * log (27 / 10)2/3) / (log 9)?
a) 0.2887
b) -0.4526
c) -0.3427
d) 0.1996
View Answer
Explanation: Given log 3 = 0.4771.
(log (0.27)2 * log (27 / 10)2/3) / (log 9) = (2(log (27 / 100)) * 2 / 3 log (27 / 10)) / 2 log 3
= (2(log 33 – log 102) * 2 / 3 (log 32 – log 10)) / 2 log 3
= (2(3 log 3 – 2 log 10) * 2 / 3 (3 log 3 – log 10)) / 2 log 3
Substituting value of log 3 as given,
= (2(3 * 0.4771 – 2) * 2 / 3 (3 * 0.4771 – 1)) / 2 * 0.4771
= (2 * (- 0.5687) * 2 / 3 (0.4313)) / 0.9542
= (- 1.1374 * 0.2875) / 0.9542
= -0.3427
2. Given the value of log 2 = 0.3010, then what would be the value of log5512?
a) 3.876
b) 2.457
c) 1.786
d) 4.924
View Answer
Explanation: log5512 = log10512 / log105
= log1029 / log10(10 / 2)
= 9log102 / (log1010 – log102)
= ((9 * 0.3010) / (1 – 0.3010))
= 2.709 / 0.699
= 3.876
3. Which of the following relationship between x and y would satisfy log(x / y) + log(y / x) = log (x + y)?
a) x – y = 1
b) x + y = 1
c) x / y = 1
d) x * y = 1
View Answer
Explanation: Given,
log(x / y) + log(y / x) = log (x + y)
➩ log ((x / y) * (y / x)) = log (x + y)
➩ log 1 = log (x + y)
➩ 1 = x + y
4. What would be the value of the expression (1 / log280) + (1 / log480) + (1 / log1080)?
a) 1
b) 2
c) 4
d) 8
View Answer
Explanation: (1 / log280) + (1 / log480) + (1 / log1080) can be written as,
➩ log802 + log804 + log8010
➩ log8080
➩ 1
5. Which value of z given in the options below would satisfy logz (5 / 7) = 1 / 3?
a) 15 / 21
b) 343 / 125
c) 125 / 343
d) 21 / 15
View Answer
Explanation: Given,
logz (5 / 7) = 1 / 3
➩ z1/3 = 5 / 7
➩ ∛z = 5 / 7
➩ z = (5 / 7)3
➩ z = 125 / 343
6. Which of the following options is the correct value for log6 ((46656) (216) / (36))?
a) 3
b) 36
c) 6
d) 7
View Answer
Explanation: Given, log6 ((46656) (216) / (36)).
➩ log6 ((66)(63) / (62))
➩ log6 (67)
➩ 7 log66
➩ 7 * 1
➩ 7
7. Given log10x = y, then how can 103y be expressed in terms of x?
a) x3
b) x2 / 2
c) 3x3
d) 3x3 / 2
View Answer
Explanation: Given,
log10x = y
➩ 10y = x
➩ 103y = (10y)3 = x3
8. Which set of values of z satisfy log (z2 – 6z + 6) = 0?
a) 1 and 2
b) 4 and 6
c) 5 and 1
d) 3 and 2
View Answer
Explanation: Given,
log (z2 – 6z + 6) = 0
➩ z2 – 6z + 6 = 100
➩ z2 – 6z + 6 = 1
➩ z2 – 6z + 5 = 0
➩ z2 – 5z – 1z + 5 = 0
➩ z(z – 5) + (- 1) (z – 5) = 0
➩ Thus, z = 1 and 5 satisfies the equation.
9. Which of the following options represent the same value as log 0.234?
a) log 2.34 + 1
b) log 2.34 – 1
c) log 2.34 / 100
d) – log 2.34
View Answer
Explanation: Given, log 0.234
➩ log 0.234 = log (2.34 / 10)
= log 2.34 – log 10
= log 2.34 – 1
10. Solve log (a – 13) + 3log2 = log (3a + 1) and tell which of the following options state the correct value of a?
a) 21
b) 24
c) 20
d) 25
View Answer
Explanation: Given,
log (a – 13) + 3log2 = log (3a + 1)
➩ log (a – 13) + log23 = log (3a + 1)
➩ log (a – 13) + log8 = log (3a + 1)
➩ log (8a – 104) = log (3a + 1)
➩ 8a – 104 = 3a + 1
➩ 5a = 105
➩ a = 105 / 5
➩ a = 21
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